Dynamic response optimization of structures with viscoelastic material using the equivalent static loads method

Abstract

Viscoelastic material is widely used in automotive structures due to its outstanding vibration-damping characteristics with appropriate stiffness. Viscoelastic material, which has viscosity and elasticity, shows energy absorption and dissipation. The material properties of viscoelastic material are dependent upon time, temperature, and loading path. Hence, these characteristics have to be considered when performing structural optimization. Studies on the constitutive equations of viscoelastic material are widely carried out, and structural optimization using harmonic excitation in the frequency-domain is often reported. However, structural optimization in the time-domain is rarely performed. One of the reasons is that the cost of sensitivity analysis is quite expensive. The Equivalent Static Loads Method (ESLM) is a linear/nonlinear dynamic response structural optimization method. In this research, a practical structural optimization method to consider the characteristics of viscoelastic material is proposed using ESLM. Equivalent static loads (ESLs) are defined as the static loads that generate the same displacement field as that from dynamic analysis. In ESLM, dynamic analysis and linear static response optimization are alternatively repeated until convergence is achieved. Viscoelastic material reduces the vibration amplitude and the stored energy in a structural system. Thus, excellent damping performance is required for a part with viscoelastic material, while the proper stiffness is maintained. An appropriate design formulation is made for the design of viscoelastic material. In this research, the sum of damping ratios, the sum of weighted damping ratios, and the sum of squared displacements are considered as the objective functions. These three objective functions deal with the peak displacements of damped vibration. Three case studies are defined by optimizations of some typical automotive parts with viscoelastic material. They are a sandwich panel, a rubber bushing, and a seat cushion. The damping performances of the objective functions are compared and discussed.

A Smooth Bidirectional Evolutionary Structural Optimization of Vibrational Structures for Natural Frequency and Dynamic Compliance

“…Published dynamic topology optimization researches mainly focus on three main problems including eigenfrequency optimization [12][13][14][15], dynamic response optimization under steady-state [16][17][18][19] and transient [20][21][22][23][24] excitations. In eigenfrequency optimization, researchers provide an efficient way such as maximization of the specified eigenfrequencies or the bandwidth to avoid structural resonance.…”

“…To efficiently solve the dynamic response in the frequency domain, the modal decomposition method is used to remarkably eliminate the computational demand for continuum structures [19]. To tackle the topology optimization problems of dynamic response in the time domain, two approaches have been developed including time-integration method scheme like Newmark-β [20,21] and the equivalent static load (ESL) method [22][23][24] so far. Generally speaking, the former has some obstacles in engineering application due to a quite time-consuming modelling, complex and challenging sensitivity analysis.…”

Modeling and analysis of dynamic characteristics of rubber isolators for electric vehicles under high-frequency excitation

“…12 Such as the Kelvin-Voigt model, Maxwell model, Berg model, and fractional derivative model. [13][14][15][16] These models can express the effect of excitation frequency and excitation amplitude on the dynamic characteristics of rubber isolators. [17][18][19] To investigate the effect of more factors on dynamic characteristics, the complex models have been established.…”

“…12 Such as the Kelvin-Voigt model, Maxwell model, Berg model, and fractional derivative model. 13–16 These models can express the effect of excitation frequency and excitation amplitude on the dynamic characteristics of rubber isolators. 17–19…”

Modeling and analysis of high-frequency dynamic characteristics of double isolation rubber mounts

“…In order to reduce the calculation time, dynamic models are usually used to describe the dynamic characteristics of rubber mounts with irregular shapes. The common dynamic models include the Kelvin-Voigt model, 16 Maxwell model, 17 generalized Maxwell model, 18 fractional derivative model, 19 and friction model. 20 Some scholars have used these dynamic models to calculate the high-frequency dynamic characteristics of rubber mounts.…”